{"paper":{"title":"Global Lorentz estimates for nonlinear parabolic equations on nonsmooth domains","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"The Anh Bui, Xuan Thinh Duong","submitted_at":"2017-02-17T02:13:15Z","abstract_excerpt":"Consider the nonlinear parabolic equation in the form $$ u_t-{\\rm div} \\mathbf{a}(D u,x,t)={\\rm div}\\,(|F|^{p-2}F) \\quad \\text{in} \\quad \\Omega\\times(0,T), $$  where $T>0$ and $\\Omega$ is a Reifenberg domain. We suppose that the nonlinearity $\\mathbf{a}(\\xi,x,t)$ has a small BMO norm with respect to $x$ and is merely measurable and bounded with respect to the time variable $t$. In this paper, we prove the global Calder\\'on-Zygmund estimates for the weak solution to this parabolic problem in the setting of Lorentz spaces which includes the estimates in Lebesgue spaces. Our global Calder\\'on-Zyg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.06202","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}